${\rm G}_2$-instantons on generalised Kummer constructions

Abstract

In this article we introduce a method to construct $\rm{G}_2$-instantons on $\rm{G}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on $\rm{G}_2$-orbifolds of the form $T^7/ \Gamma$. We use this construction to produce non-trivial examples of $\rm{G}_2$-instantons.